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Chaminade University of Honolulu Physics 152 Laboratory Charging and Discharging Capacitors I. INTRODUCTION A. A capacitor is composed of two conductors separated by an insulator, called a dielectric, and has the capacity to store electrical charge and energy. A capacitor is charged when the two conductors have equal but opposite charges. The charged capacitor can hold or store this charge and since the conductors have opposite charges there is an electrical potential energy difference between them. This electrical potential energy difference increases as the stored charge increases. The ratio of the magnitude of stored charge (Q) to the magnitude of the electrical potential energy difference (V) is a positive constant for a capacitor. This constant is called the capacitance, C = Q/V. B. The units of capacitance are coulombs/volt, which is called a farad. The larger the capacitance the more charge the capacitor may store per given electrical potential energy difference. The capacitance is a function of several factors 1) the geometry of the conductors 2) the insulating material, the dielectric, between the conductors (a) compared to the electric field E0 between the conductors that are separated by a vacuum, a dielectric is characterized by a (dielectric) constant, , that reflects a decrease in the electric field between the conductors: E = E0/, when the dielectric, instead of vacuum, separates the conductors. (Note that is greater than 1 for electrically insulating materials, and that it is defined as 1 for a vacuum). The decrease in electric field is proportional to a decrease in electrical potential energy difference V (versus V0, that is V = V0/) between the conductors. Basically, the dielectric undergoes polarization induced alignment of dipoles that results in a shielding of the electric field between the conductors. Overall, the capacitance increases with the insertion of a dielectric versus vacuum. (See Table 20-1, p. 665) i. Insertion of a dielectric into a charged capacitor, that is the capacitor is disconnected from a battery source after being charged, decreases V (versus V0) without affecting the stored charge Q. Therefore, since C = Q/V, C has to increase-by the factor . ii. Insertion of a dielectric into a capacitor that is being charged, that is the capacitor containing the dielectric is connected to a battery source, would require more charge Q (versus Q0, that is Q = Q0*) to build up on the conductors, in order to reach the same potential V as that of the battery. Therefore, since C = Q/V, C has to increase-by the factor . (b) There is maximum value of electric field, called the dielectric strength, to which a dielectric can withstand without dissociation on an atomic level. If this value of electric field is surpassed, the Page 1 of 6 japjr-created 03/25/04 modified 03/25/04 Chaminade University of Honolulu Physics 152 Laboratory Charging and Discharging Capacitors dielectric will break; the process called dielectric breakdown. (See Table 20-2, p.667) C. The work necessary to charge a capacitor, comes from the energy of a voltage source, (e.g. the chemical energy of a battery), and is converted to electrical potential energy within the electric field of the capacitor; the field between the conductors. Note that a capacitor can build up an electrical potential energy difference equal to that of the charging source, but that it can discharge its stored energy must faster, which leads to a larger power output than possible with the voltage source. D. Charging a capacitor requires charging each conductor individually, since ideally charge does not travel through the insulating material between the conductors of a capacitor 1) The connection of a capacitor to a battery source nearly instantaneously charges the conductors of the capacitor to an electrical potential energy difference of the same magnitude and polarity as that of the battery. Note by the definition of capacitance, that the total charge accumulated on the capacitor is Q = CV or Q = C. 2) The addition of resistors in series with the capacitor of the circuit increases the charging time required for the capacitor. Furthermore, the electrical potential energy drop across the resistor (see Laboratory Experiment Ohmic resistors) causes the electrical potential energy drop across the capacitor to be less than that of the battery source. (a) - IR – Q/C = 0 (Kirchoff’s voltage loop rule) (b) I0 = / R (At the instant the RC elements are connected to the battery, there is not yet any Q on the capacitor. At this time, the electrical potential energy drop is only across the resistor.) (c) Q = C(Later when the capacitor becomes fully charged, there is no longer any current flowing: I=0. The electrical potential energy drop is entirely across the capacitor.) E. Mathematical operations on the equation of D.2)(a) yields analytical expressions for charging the capacitor. Page 2 of 6 japjr-created 03/25/04 modified 03/25/04 Chaminade University of Honolulu Physics 152 Laboratory Charging and Discharging Capacitors Page 3 of 6 japjr-created 03/25/04 modified 03/25/04 Chaminade University of Honolulu Physics 152 Laboratory Charging and Discharging Capacitors Page 4 of 6 japjr-created 03/25/04 modified 03/25/04 Chaminade University of Honolulu Physics 152 Laboratory Charging and Discharging Capacitors F. For the discharging of a charged capacitor, we must remove the battery from the circuit and substitute a switch that is left open. In this case, we are left with a charged capacitor with a voltage drop of Qmax/C but zero electrical potential energy drop across the resistor because there is no current flowing. Closing the switch will allow the capacitor to discharge through the resistor. At any time during this process, the current in the circuit is I and is equal to the rate of decrease of charge Q on the capacitor. This current then puts a potential electrical energy difference across the resistor. At any given time the potential electrical energy differences across these two circuit elements are equal: IR = Q/C (Kirchoff’s voltage loop rule). Mathematical operations on this equation yield analytical expressions for discharging the capacitor. Page 5 of 6 japjr-created 03/25/04 modified 03/25/04 Chaminade University of Honolulu Physics 152 Laboratory Charging and Discharging Capacitors II. OUTLINE A. Form an RC circuit with one voltage source, one capacitor, one resistor and a single-pole, double-throw switch. B. Measure and record voltage drops across the capacitor during charging and discharging. C. Observer current in the circuit, particularly direction during these processes as well as the voltage drop across the resistor. III. PROCEDURE A. Setup the RC circuit as directed with an ammeter and voltmeter inserted. B. Use the single-pole, double-throw switch to charge the capacitor through the resistor with the battery. 1) Note the direction of current. 2) Note the voltage drop across the resistor. 3) Record in Table 1 of the Data Sheet the buildup of the electrical potential energy difference across the capacitor every 5-10s until the capacitor’s electrical potential energy difference asymptotes off to a constant value. C. Use the single-pole, double-throw switch to discharge the capacitor through the resistor and breaking contact with the battery. 1) Note the direction of current. 2) Note the voltage drop across the resistor. 3) Record in Table 1 of the Data Sheet the decrease of voltage across the capacitor every 5-10s until the capacitor’s electrical potential energy difference asymptotes off to a constant value. D. Determining the RC time constant. 1) Based on the data of Table 1 in the Data Sheet, calculate the values of - V and ln( - V) as outlined in the INTRODUCTION for charging of a capacitor. (a) Record these values in Table 1 of the Results Sheet. (b) Plot this data to determine the RC time constant. (c) Compare to the given values of R= and C= as a percent error. (Note that resistance can be expressed as volts/coulombs/seconds and that capacitance can be expressed as coulombs/volts, so that the product is in units of time.) 2) Based on the data of Table 1 in the Data Sheet, calculate the values of ln V(t) and of ln Vmax as outlined in the INTRODUCTION for discharging of a capacitor. (a) Record these values in the Table 2 of the Results Sheet. (b) Plot this data to determine the RC time constant. (c) Compare to the given values of R= and C= as a percent error. Page 6 of 6 japjr-created 03/25/04 modified 03/25/04

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posted: | 7/8/2010 |

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